Locus Options

As covered previously the loci an instrument covers can be easily found given details such as angular range and initial energy.

Figure 3.26: Creating experimental loci

(a)The locus options GUI

(b)Scatter data over a loci starting at 10◦ to 160◦ with an initial energy of 5meV

Using the Locus Options window, which is shown to the user by Contour Button (4), instrument loci can be applied to Scatter data. This is useful for

planning experiments as the user can check if features predicted by Scatter are covered. It is also useful in interpreting experimental data, this functionally is highlighted in the Graphite chapter.

The loci are found using equation (3.2) once again and the user then has the option of showing just the loci as demonstrated in the Instruments section, the loci applied to Scatter data as demonstrated in figure (3.26b) or Scatter data overlayed on experimental as demonstrated in figure (3.27).

Figure 3.27: Contours of Scatter data, over graphite IN5 measurement

The application of Neutronplot to the analysis of poly-CINS data is shown in chapters 4 and 5.

Chapter

4

Structure of Graphite Based

Materials

4.1

Graphite Background

In this chapter we will investigate the structure of several natural graphite powder samples. Historically the study of the structure and dynamics of graphite focused on the perfect crystal, this was followed by studies of var- ious artificial graphitic materials such as those suitable for use as neutron moderators. The natural graphite samples allow us to investigate the defects in graphite. We will particularly focus on stacking faults such as the rhom- bohedral and turbostratic structures present in these samples. We will also investigate how the structure of an expanded graphite derived from natural graphite is changed by the processes it has undergone.

Graphite was amongst the earliest materials studied using x-ray diffraction with measurements taken by both Bragg[31] and Ewald[32] in 1914. The struc- ture of graphite was confirmed in 1924 by Bernal[33]. Investigations into the behaviour and structure of graphites continued, peaking during the creation of graphite moderated reactors. The study of graphite then waned but was

recently revived with the discovery of fullerenes and the need to investigate the end of life of nuclear reactors.

Figure 4.1: The structure of hexagonal graphite created in Materials Studio

(a)Hexagonal graphite structure viewed

perpendicular to graphene planes

(b)Hexagonal graphite structure showing layered structure and stacking

Perfect crystalline graphite is comprised of carbon atoms in a hexagonal lattice structure. It has the space group P63/mmc and lattice parameters of a=2.461 Å andc=6.708 Å giving a plane to plane distance of 3.354 Å.

Atoms are arranged in sheets with strong sp2 covalent bonding between the atoms in the layer, leaving free electrons in the material allowing graphite to act as a conductor. Layers are weakly bound to each other by Van der Waals interactions. The high anisotropy in graphite means that its properties vary depending on the orientation of the sample with phonons travelling quickly in the layers but slowly between. Graphite has a high melting point and a low thermal conductivity perpendicular to the plane. Its electrical properties lead to its use as an electrode and in batteries. It has a low neutron absorption cross-section and is therefore used as a moderator.

with possible non-carbon impurities. Graphite can experience mechanical forces in the earth creating areas of rhombohedral and turbostratic graphites. These can be annealed fully or partially due to heating of the material far un- derground. Geologists study the structure of natural graphite to discover the geological history of the areas in which it is found[34]. As natural graphite sam- ples can contain elements of different graphite structures, we will investigate the structure of Highly Ordered Pyrolytic Graphite (HOPG), rhombohedrally stacked graphite and turbostratic graphite, to aid understanding of the full structure of natural graphite.

Figure 4.2: Two of the 00l planes in the hexagonal lattice shown in the graphite structure

(a)The 001 planes of the hexago- nal lattice

(b)The 002 planes of the hexago- nal lattice

There are several important planes of atoms present in the graphite lattice which give rise to peaks in the graphite XRD pattern. The 00l planes are parallel to the layers of carbon atoms in graphite. Odd 00l directions do not correspond with layers of atoms and so give no peaks in a diffraction measure- ment. Even 00lreflections do correspond with atomic planes and the 002 plane gives the most intense diffraction peak of these reflections and generally the whole XRD measurement, depending on orientation and the disorder in the sample. The 00l peaks give information about the spacing of graphene layers

in graphite. The broadness and position of the peaks can give information on the range of interlayer widths which is related to the level of disorder in the material.

Figure 4.3: hklplanes of the hexagonal lattice shown in graphite

(a)The 100 planes of the hexagonal lat- tice

(b)The 102 planes of the hexago- nal lattice

Other planes in the hexagonal lattice are the hk0 planes such as 110, 100 and 010. These directions are equivalent and are perpendicular to the 00l reflec- tions. The hk0 planes give information about the distance between atoms within the graphene plane.

Other planes cover directions both in and perpendicular to the graphite plane such as the 101 102 and 212 directions. Peaks arising from these planes will be seen in following diffraction measurements.

As our measurements are on powder samples, as discussed in the theory chap- ter, this should mean the effects of orientation are removed as all planes are distributed equally. However in practice the shape of the powder particles affects how the planes are orientated with respect to the diffraction surface. Natural graphite shows substantial peak broadening particularly on the 00l peaks as graphite is particularly susceptible to changes of graphene interlayer distance due to the weak bonding between these layers.